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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
95.1.d.a	$95$	$1$	95.d	95.d	$2$	$1$	$1$	$0.047$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots$
95.1.d.b	$95$	$1$	95.d	95.d	$2$	$2$	$2$	$0.047$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
475.1.c.a	$475$	$1$	475.c	19.b	$2$	$1$	$1$	$0.237$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-2q^{11}+q^{16}-q^{19}+\cdots$
475.1.c.b	$475$	$1$	475.c	19.b	$2$	$2$	$2$	$0.237$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{2}-\beta q^{3}-q^{4}-2q^{6}-q^{9}+\beta q^{12}+\cdots$
760.1.b.a	$760$	$1$	760.b	760.b	$2$	$8$	$8$	$0.379$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}q^{2}+(\zeta_{16}^{3}+\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots$
855.1.g.a	$855$	$1$	855.g	95.d	$2$	$1$	$1$	$0.427$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+2q^{11}+q^{16}+q^{19}+\cdots$
855.1.g.c	$855$	$1$	855.g	95.d	$2$	$2$	$2$	$0.427$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\beta q^{2}+q^{4}+q^{5}-\beta q^{10}+\beta q^{13}+\cdots$
855.1.z.a	$855$	$1$	855.z	855.z	$6$	$2$	$1$	$0.427$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$-1$	$1$	$-1$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
855.1.z.b	$855$	$1$	855.z	855.z	$6$	$2$	$1$	$0.427$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
855.1.z.c	$855$	$1$	855.z	855.z	$6$	$4$	$2$	$0.427$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}-\zeta_{12}q^{3}+(-1+\cdots)q^{4}+\cdots$
855.1.z.d	$855$	$1$	855.z	855.z	$6$	$8$	$4$	$0.427$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{11}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
1045.1.w.a	$1045$	$1$	1045.w	1045.w	$10$	$4$	$1$	$0.522$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$-2$	$-2$	$-1$	$0$	$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
1045.1.w.d	$1045$	$1$	1045.w	1045.w	$10$	$4$	$1$	$0.522$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$2$	$2$	$-1$	$0$	$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
1045.1.w.e	$1045$	$1$	1045.w	1045.w	$10$	$8$	$2$	$0.522$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$5$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{3}+\cdots$
1045.1.w.f	$1045$	$1$	1045.w	1045.w	$10$	$16$	$4$	$0.522$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{11}+\zeta_{40}^{13}+\cdots)q^{3}+\cdots$
1140.1.p.e	$1140$	$1$	1140.p	1140.p	$2$	$8$	$8$	$0.569$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{7}q^{3}-\zeta_{16}^{2}q^{4}+\cdots$
1140.1.p.f	$1140$	$1$	1140.p	1140.p	$2$	$8$	$8$	$0.569$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}q^{2}-\zeta_{16}^{5}q^{3}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{4}q^{5}+\cdots$
1235.1.e.e	$1235$	$1$	1235.e	1235.e	$2$	$8$	$8$	$0.616$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}^{3}-\zeta_{16}^{5})q^{2}+(\zeta_{16}-\zeta_{16}^{7}+\cdots)q^{3}+\cdots$
1235.1.bd.a	$1235$	$1$	1235.bd	1235.ad	$6$	$2$	$1$	$0.616$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$-2$	$1$	$2$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+3\zeta_{6}^{2}q^{4}+q^{5}+\cdots$
1235.1.bd.b	$1235$	$1$	1235.bd	1235.ad	$6$	$2$	$1$	$0.616$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$2$	$-1$	$2$	$0$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+3\zeta_{6}^{2}q^{4}+q^{5}+\cdots$
1235.1.bd.c	$1235$	$1$	1235.bd	1235.ad	$6$	$4$	$2$	$0.616$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
1235.1.bd.d	$1235$	$1$	1235.bd	1235.ad	$6$	$8$	$4$	$0.616$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$-8$	$0$	$1$		$q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{2}+(\zeta_{24}^{7}+\zeta_{24}^{9}+\cdots)q^{3}+\cdots$
1235.1.bm.a	$1235$	$1$	1235.bm	1235.am	$6$	$16$	$8$	$0.616$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{48}^{13}+\zeta_{48}^{19})q^{2}+(-\zeta_{48}^{15}+\cdots)q^{3}+\cdots$
1425.1.j.a	$1425$	$1$	1425.j	285.j	$4$	$2$	$1$	$0.711$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-1-i)q^{2}-iq^{3}+iq^{4}+(-1+\cdots)q^{6}+\cdots$
1425.1.j.b	$1425$	$1$	1425.j	285.j	$4$	$2$	$1$	$0.711$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$-2$	$2$	$0$	$0$	$1$		$q+(-1-i)q^{2}+q^{3}+iq^{4}+(-1-i+\cdots)q^{6}+\cdots$
1425.1.j.c	$1425$	$1$	1425.j	285.j	$4$	$2$	$1$	$0.711$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$2$	$-2$	$0$	$0$	$1$		$q+(1+i)q^{2}-q^{3}+iq^{4}+(-1-i+\cdots)q^{6}+\cdots$
1425.1.j.d	$1425$	$1$	1425.j	285.j	$4$	$2$	$1$	$0.711$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(1+i)q^{2}+iq^{3}+iq^{4}+(-1+i+\cdots)q^{6}+\cdots$
1425.1.j.e	$1425$	$1$	1425.j	285.j	$4$	$4$	$2$	$0.711$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{285}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{9}+\zeta_{8}q^{12}+\cdots$
1425.1.j.f	$1425$	$1$	1425.j	285.j	$4$	$4$	$2$	$0.711$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{57}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}-3\zeta_{8}^{2}q^{4}+2q^{6}+\cdots$
1520.1.m.a	$1520$	$1$	1520.m	95.d	$2$	$1$	$1$	$0.759$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{5}-q^{9}+2q^{11}-q^{19}+q^{25}+\cdots$
1520.1.m.b	$1520$	$1$	1520.m	95.d	$2$	$2$	$2$	$0.759$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{3}-q^{5}+q^{9}-\beta q^{13}+\beta q^{15}+\cdots$
1520.1.bh.c	$1520$	$1$	1520.bh	1520.ah	$4$	$16$	$8$	$0.759$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{3}q^{2}+(\zeta_{32}-\zeta_{32}^{7})q^{3}+\zeta_{32}^{6}q^{4}+\cdots$
1805.1.h.a	$1805$	$1$	1805.h	95.h	$6$	$2$	$1$	$0.901$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{9}-q^{11}+\cdots$
1805.1.h.b	$1805$	$1$	1805.h	95.h	$6$	$4$	$2$	$0.901$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
1805.1.o.a	$1805$	$1$	1805.o	95.o	$18$	$6$	$1$	$0.901$	$\Q(\zeta_{18})$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $		$24$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{4}-\zeta_{18}^{7}q^{5}-\zeta_{18}^{8}q^{9}+\cdots$
1805.1.o.b	$1805$	$1$	1805.o	95.o	$18$	$12$	$2$	$0.901$	12.0.$\cdots$.2	$D_{4}$	$\Q(\sqrt{-95}) $	None		$24$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{5}+\beta _{11})q^{2}+\beta _{5}q^{3}+(-\beta _{4}-\beta _{10}+\cdots)q^{4}+\cdots$
1900.1.j.a	$1900$	$1$	1900.j	380.j	$4$	$8$	$4$	$0.948$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}+(-\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots$
1900.1.j.b	$1900$	$1$	1900.j	380.j	$4$	$8$	$4$	$0.948$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}+(\zeta_{16}+\zeta_{16}^{3})q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
2280.1.t.a	$2280$	$1$	2280.t	2280.t	$2$	$1$	$1$	$1.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-95}) $, $\Q(\sqrt{-570}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
2280.1.t.b	$2280$	$1$	2280.t	2280.t	$2$	$1$	$1$	$1.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-95}) $, $\Q(\sqrt{-570}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$-1$	$1$	$1$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
2280.1.t.c	$2280$	$1$	2280.t	2280.t	$2$	$1$	$1$	$1.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-95}) $, $\Q(\sqrt{-570}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$1$	$-1$	$1$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
2280.1.t.d	$2280$	$1$	2280.t	2280.t	$2$	$1$	$1$	$1.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-95}) $, $\Q(\sqrt{-570}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$1$	$1$	$-1$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
2280.1.t.e	$2280$	$1$	2280.t	2280.t	$2$	$2$	$2$	$1.138$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-95}) $, $\Q(\sqrt{-114}) $	$\Q(\sqrt{30}) $		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}+iq^{8}+\cdots$
2280.1.t.h	$2280$	$1$	2280.t	2280.t	$2$	$2$	$2$	$1.138$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-95}) $, $\Q(\sqrt{-114}) $	$\Q(\sqrt{30}) $		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}+q^{5}-q^{6}+iq^{8}+\cdots$
2280.1.t.i	$2280$	$1$	2280.t	2280.t	$2$	$4$	$4$	$1.138$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}-q^{5}+\cdots$
2280.1.t.j	$2280$	$1$	2280.t	2280.t	$2$	$4$	$4$	$1.138$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+q^{5}-\zeta_{8}^{2}q^{6}+\cdots$
2375.1.c.a	$2375$	$1$	2375.c	19.b	$2$	$4$	$4$	$1.185$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(\zeta_{10}+\zeta_{10}^{4})q^{3}+\cdots$
2375.1.c.b	$2375$	$1$	2375.c	19.b	$2$	$4$	$4$	$1.185$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots$
2375.1.c.c	$2375$	$1$	2375.c	19.b	$2$	$8$	$8$	$1.185$	8.0.1024000000.1	$D_{20}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{7}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}-\beta _{4}q^{6}+\cdots$
2375.1.d.a	$2375$	$1$	2375.d	95.d	$2$	$2$	$2$	$1.185$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-95}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.